1. Polarization
Updated 2014Nov17
Dr. Bill Pezzaglia
Light & Optics

2. Outline 2 Linear Polarization Polarization Detection
Hertz Waves
Linear Polarization Modes
Polarization by Reflection
Polarization Detection
Detecting polarized Light (Malus’ Law)
Optical Activity
Birefringence
Circular Polarization
Quarter Wave Plate
Left & Right Circular Polarized Light
Detecting Circular Polarized Light (3D movies!)
Fresnel’s Equations
Fresnel’s Reflection Equations
What we measure in lab
References

3. Linear Polarized Light Polarization by Reflection
A. Linear Polarization 3
Hertz Waves
Linear Polarized Light
Polarization by Reflection

4. 1. EM Hertz Wave Equation 4
(a) Maxwell shows his equations predict that electromagnetic waves can exist in vacuum (note E & B are perpendicular to each other and direction of wave)

5. 2. Linear Polarization 5
[1812 Fresnel develops wave theory of transverse polarized light, well before the electromagnetic nature was known]
light has two perpendicular linear polarizations (electric field) can be horizontal or vertical Hertz shows electromagnetic waves have transverse polarization (equivalent to “light”)

6. 3. Polarization by Reflection6
1808 Malus’s Law: Reflected light is often polarization
1812 Fresnel develops wave theory of transverse polarized light
1815 Brewster’s angle: at this angle of incidence the reflected light is entirely “s” polarized such that electric field is parallel to the interface surface
Note: “Plane of incidence” is the plane defined by the three beams above.
The normal also lies in this plane. The plane is perpendicular to the surface.

7. B. Detection of Polarization7
Detection, Malus’ Law
Optical Activity
Birefringence

8. 1. Detecting Polarized Light8
Linear polarizer can be used to detect polarized light, only lets one polarization through!
1808 Malus’s Law: Linear polarized light passing through a second polarizer tilted at angle  to first will be attenuated:
Hence no light gets through “crossed polarizers” (=±90°)

9. 2. Optical Activity 9
Optically active materials can rotate the polarization
If such a substance is put between “crossed polarizers” (90º angle) you will often see interesting colors.

10. 3. Birefringence 10
1669 Erasmus Bartolinus (Denmark) discovers the birefringence (double refraction) of calcite crystals.
When polarization was understood better, it was realized the two different polarizations took different paths (they are “refracted” differently, or the index of refraction is dependent upon polarization)
Index of refraction: n=c/v, so the different polarizations travel at slightly different speeds.

11. C. Circular Polarized Light11
Quarter Wave Plates
Left & Right circular polarized
Detecting circular polarized

12. 1. Quarter Wave Plates 12
A quarter wave plate retards horizontal polarization by 90º to vertical. It can be used to make circular polarized light from linear polarized light.

13. 2. Circular Polarized Light13
Another type of polarized light can be left or right handed circular polarized

14. 3. Detecting Circular Polarized Light14
A quarter wave plate will turn circular back into linear, which can be detected by a linear polarizer

15. D. Fresnel Equations Fresnel Reflection Equation15
Fresnel Reflection Equation
Brewster’s angle (lab)

16. 1. Fresnel’s equations 16
Fresnel’s equations generally show that the amount of light reflected is a function of the angle of incidence.
Further, the different polarizations of light have different reflective equations.
In particular, he shows that at Brewster’s angle, the “p” wave (electric field parallel to plane of incidence) has no reflectance, hence the reflected rays are entirely “s” polarized (electric field perpendicular to plane of incidence, which is parallel to surface)

17. 2. Brewster’s Angle 17
At Brewster’s angle Rp=0. This and Snells’ law gives you:
Square both, and use the Pythagorean identity.
Solving, we get Brewster’s angle: (approx 56 for glass)

18. 18
References

19. Things to Do 19 Find tesla museum stuff
Who first predicted circular polarized light?
Can we make a 3D image for students using polarized light? Need two projectors?
Ideally we’d use circular polarized light, but one test so far shows either the transparency projector or the screen does not preserve the circular polarization.